Electric wave filter



P 5.1.. NORTON" 1,708,950

ELECTRI C WAVE FILTER Original Filed May 12, 1925 MWWWWT fM MMA/WW AW Patented Apr. 16, 1929:

UNITED STATES EDWARD I]. NORTON, OF NEW YORK, N. 'Y.,

WESTERN ELECTRIC COMPANY,

I ELECTRIC WAVE FILTER.

Application filed May 12, 1925, Serial No. 29,690. Renewed March 16, 1828.

This invention relates to wave filters and more particularly to filters having wave transforming properties.

The object of the invention is to permit highly eflicient and selective transmission of a band of waves havin definite limiting freguencies, between terminating impedances of iiferent magnitudes. 1 p

The principles involved in the invention 1 are broadly disclosed in copending application 751,748 filed Nov. 24, 1924 (which became Patent 1,681,554, Aug. 21, 1928) of which the present application is a continuation in part, with particular reference to types of filters embodying one species of the invention. In thepresent specification a number of examples will'be illustrated and described of filters embodying a different specific form of the broad invention, the scope of the present invention being pointed out in the claims.- v

The type of wave filter with respect to which invention is disclosed is that invented by G.A. Campbell and described in his U. S.

Patent No. 1,227 ,113 issued May 22, 1917 the unique feature of which is that it permits the transmission-through a system'of a band of waves betweendefinite limits of frequency and discriminates sharply against waves having frequencies outside the band. For further information regarding the theory of this filter and the design of many specific forms reference is made to the following published articles; Physical theory of the electric wave filter-'G. A- Campbell, Bell sy tem Technical Journal, Vol. I, No.- 2, November'1922; The theory and designof uniform and composite wave filters,-O. J. Zobel, BellSystem Technical Journal,-'Vol. II No. 1, January 1923;, and, Transmission characteristics of ele ctric'wave filters-O. J. Zobel, Bell System Technical Journal, Vol. III, No. 4, October 1924. I

In these references the principle is developed that the propertiesof an included portion of an infinite transmission line, consisting of a sequential arrangement of homologous four-term1nal networks, may be identical with the self. properties of the individual 5 networks.- It'is also shown, particularly in the reference last mentioned, that the trans-. mission properties of a system comprising a finite number of similar networks terminated in any arbitrary impedances may be readil computed in terms of certain simple'over-al l properties of the networks, whereb the laborious, process is avoided of obtaimn a solution in terms of theparameters of t e elementary components of the networks.

By this method of attack the rules for proportioning networks to secure various types of broad band selectivity have been discovered and'set forth in simple form, and networks of many ypes have been devised having band filter properties of various kinds. 5

Althoif h the filter characteristics of the mdividua -networks, or sections, are exactly reproduced onl in the infinitely extended line, it has been ound that the are reproduced with great accuracy in a nite system comprising a limited number of sections connected between resistive terminating impedances and are present to a controlling degree even when only one section is' included be tween the termlnating resistances. The case of resistive termination is one of great'practical interest and importance since wave generators and receivers must necessarily be substantially free from reactance to achieve high efiiciency in performing their functions.

Hitherto filter systems have beendesigned and constructed to operate efficiently between equal terminating impedances and in the event that the terminating impedances were necessarily unequal one or more transformers have been used to transform the impedances ac 23 equal values suitable for terminating the tar.

In accordance 'with the'present invention the transformation is accomplished by the filter itself and the need for additional transforming devices is eliminated.

The invention will be fully understood from the following detailed description taken in connection withjthe accompanying drawings of which Figures 1 and 2 illustrate a theorem n which the invention is based,

Figures 3, 4 and 5 ill ustratespecific forms I I of wave transforming filter sections haying the same configurations as their non-transforming prototypes,

Figures 6 and 7 illustrate other specific forms of Wave transforming filters of which the non-transforming prototype is shown in Figure 8,

Figures 9 and 10 show respectively an .ductance and of zero resistance and should be perfectly coupled together. The induct-ances, although each is infinitely great, should have a finite ratio depending on the transformation ratio desired.

The network of Fig. 2, in which the combination of Z and the ideal transformer is replaced by a II network of impedances Z Z and Z is equivalent to that of Fig. 1 with respect to the transmission of waves between the terminating impedances Z and Z provided that the following relationships exist bet-ween the impedances of the two systems;

in which of: is the step-up voltage transformation rat-i0 of the ideal transformer, or is the ratioof the inductance of the secondary winding S to that of the primary winding P.

It should be noticed that the sum of the lmpedances Z Z and Z is zero and that Z;, and Z are in the ratio.

The proof of the equivalence of the two circuits may be established by the application of Kirchoffs laws to determine in each case the current in the impedance Z corresponding to an impressed electromagnetic force E in series with Z In the network of Fig. 1 the assumption of ideal transformer properties gives the solution 1 denoting the current in the impedance Z The direct solution of the network of Fig. 2 gives for the received current, denoted by the value which, when simplifiediby substitutingthe values given by Equations 1 for Z,,, Z and Z and by noting that the sum of these impcdances is zero,.becomes identical with the value given by Equation 2.

By a similar procedure it may also be shown that the two input currents I and l are equal, thereby completely establishing the equivalence of the two networks with respect to wave transmission from Z to Z The equivalence of the two for wave transmission in the opposite direction follows directly from the principle of reciprocity, or it may be separately established by the meth ods already described.

The impedances Z,,, Z, and Z are all of like type and of the same type as Z for example, if Z consists of an inductance Z Z and Z would also be of the nature of inductanccs. But, one of the inductanccs, either Z or Z, depending upon whether the ratio is less or greater than unity, must be negative, and consequently to construct a physical circuit exactly in accordance with Fig. 2 it would be necessary to have a new kind of circuit element, namely a negative induc tance.

The construction of networks in accordance with Fig. 2 in its most general sense would require not only negative inductances but also negative capacities and resistances. It has been customary to speak of a capacitive react-ance as negative and of an inductive rcactance as positive, and out of this there has grown a practice of regarding an inductance as a negative capacity and vice versa. A capacity, however, can correspond to a negative inductance at one wave frequency only and therefore cannot be used as a negative inductance element in the transforming network. The negative elements required to make the network of Fig. 2 universally equivalent to that of Fig. 1 must in each case correspond to constant positive elements. and as such elements are not at present available the construction of the transforming network as a separate physical entity is practically impossible.

If, however, the network is included in anextcnded system it may be so construed that the negative elements can be absorbed in or overbalanced by positive elements of the proper type whibh form essential parts of the system. Under these circumstances the desired transforming effect may be fully realized. I I

Wave filters of the types described in the references mentioned in an earlier part of this specification are especially adapted to modification by means of the transforming network the result of the modification being the production of new types of filter in which the waves are transformed in intensity while the selective characteristics remain unaltered.

Examples of wave transforming filters are shown inFigs. 3 to 7 inclusive and Fig. 9. In each example a single section is shown included between unequal terminating impedances Z and Z,. The meaning of the term section as applied to recurrent wave filters is defined in the aforementioned references in which the various types of section with respect to the mode of termination are also described to filters of the so-called ladder type which comprise a tandem arrangement of similar series impedances and similar shunt impedances. In a ladder type structure of the repeated, or uniform, type the most important sections are the mid-series and the mid-shunt sections. The mid-series section in its generalized form is a T-network comprising two equal series impedances, each being equal to one half of the impedance of a complete series branch of the repeated struc-' ture, and a shunt impedance e ual to the impedance of a complete shunt ranch of the repeated structure. The mid-shunt sect-ion is obtained, as it were, by cleaving the repeated structure through the middle of two successive shunt impedances; it therefore consists of a H network having two shunt impedances each equal to, twice the impedance of a complete shunt branch and a full series branch impedance connected therebetween.

Important characteristicsof the uniform filter sections are the iterative impedance and the propagation constant, These are most conveniently defined with reference to an infinitely long uniform filter for the reason that the properties of the infinite filler are most simply related to the self properties of the individual section. p

The iterativeim fedance is the impedance looking into the in nitel extended filter. If the filter be extended in nitely in both directions it may be conceived that a cleavage is made at some arbitrary point and the impedance of one or both portions is measured at the cleavage. There is an indefinite num ber'of iterative impedances which depend upon the particular point'at which the cleavage is made. If it is made at mid-shunt the impedances of both portions of the doubly extended line will be equal, and so also if the cleavage is made at mid-series. This symmetry is uniquely characteristic of the two points of section and in consequence the mid- I series and mid-shunt iterative impedances acquire special importance.

Anothendistlnctive characteristic of the mid-section terminations is that in selective circuits, such'as wave filters, in which the elements are purely reactive the character of the iterative impedance is closely related to the selectivity characteristic of the circuit.

Within the limits of the pass-bands the iterative impedances are purel resistive, and in the frequency ranges in" w ich waves are attenuatedthe iterative impedances are purely reactive.

,In addition to this it should be noted that the mid-shunt and mid-series sections of a uniform filter are symmetrical with respect to the input and the output terminals.

The wave transforming filter sections of the present invention, on account of their transforming properties, are unsymmetrical structures with respect to their input and output terminals. Their mode of operation andthe method of determining the design is, however,

most readily understood by considering howthey are related to symmetrical sections of uniform filters.

Referring to Fig. 3, the network included between the dotted lines B, B and C, C may be considered as a connecting link between an extended low impedance filter, represented b the generalized impedance Z and an exten ed high im edance filter represented by Z.

These two lters may be assumed to comprise uniform sections of the same general form as the connecting circuit.

The connecting circuit could be constructed in two parts, one part being designated simply as an extension of the low impedance filter and the other to match the high imped-' ance filter. The two parts could then be coupled toether, for example at the section'AA', throu h a transformer having an appropriate transfbrmation ratio and possessing as fully as possible the properties of an ideal transformer. 1

If this is done the connecting circuit will include a combination of the type illustrated in Fig. 1, namely a series impedance constituted by the series condenser and an ideal transformer. It will cause no change in the char-- acteristics of the system, therefore, if the equivalent networkof three capacities in accordance with Fig. 2 is substituted for the combination. The negative capacity of the transforming network may,'in this case, be combined with the positive capacity of one of the shunt branches to sultant. I

To elucidate further the procedure outlined in the foregoing paragraphs, design formulae for the filter section of Fig. 3 will be de-- veloped in detail.

Since the procedure is-not afl'ectedby the particular nature of the terminating impedproduce a positive reances Z and Z it may be assumed that they represent transmission lines having resistive impedances R and R respectively. The filter'section will first be computed as a symflow of energy t rough the following formulae in which f and f denote respectively the lower and the upper limiting frequencies of the transmission band.

' The derivation. of these formulae is explained by O. J. Zobel, Theory and design of uniform and composite electric wave filters,

Bell System Technical Journal Volume II No. 1, January 1923, the formulae relatin to Fig. 3 being shown in -Appendix II 5 tion V.

If, now, it is assumed that the wave transforming property is to be secured by inserting an ideal transformer at the section AA, the best value of the transformation ratio 4 is that corres ending to the maximum system, and is defined by the equati'oii' The insertion of'the transformer requires that the part of the filter section to the right v of AA be increased in impedance in the ratio 12. This requires that the value of L, be multiplied by andthe value of O,

' be divided by 13.

r .The next step of substituting, for .the combination of series capacity 0', and the ideal transformer the equivalent transforming network, leads direetly to the final design.

The series capacity 0 is equal-to the capacity, 0, first computed decreased in the ratio 1: Since the transforming network comprises capacity elements the impedances are increased int ersely as the capacities are reduced, hence the multiplying factor involving the ratio -in Equation 1 must be inverted to give the capacity values in terms of 6" The left hand shunt capacity 0, is equal quency they willbe in the ratio 1 4?.

to the result-ant of capacity 0', in parallel with a positive capacity having the value 0, 1) qb, and the right hand shunt capacity 0,, is the resultant of the parallel combination of the capacity O' and a negative capacity 0', (1)

The values may now be written down as follows:

By means of Equation (4:) these values may be expressed inte'rms of the me resistance and the cutoff frequencies, for example:

An inspection of Equation (7) shows that for large values of the resultant capacity may'become negative and that there is consequently a limiting value of the transformation ratio which cannot in practice be exceeded. The limiting value, denoted by 4 is given by the equation 4 This value of the-limiting ratio is not general but refers only to the network of Flgure 3 and to certain closely related networks.

' The value in any other specific case may be computed quite readily by equating the magnitude of the'negative element in the transforming network'to the magnitude of the positive element with which it is to be com- The reasoning process described above in connection with the design of the section renders it self-evident that the wave selection properties of the filter are maintained.

Certain impedance properties of the section will now be considered.

It may be assumed that the impedance Z comprises an infinite se uence of symmetr cal mid-shunt sections of the same schematic type as the coupling section and designed in accordance with Equation (4) for an impedance R Theimpedance Z may likewise be assumed to com rise a similar filter designed for an impe ance R Under such circumstances the lmpedances measured on both sides of the section BBv will be equal and so also will the impedances on both sides of the section CC. At the latter section however the impedances willbe 49 times greater than at the former section, that is the impedances at both sections will have the same kind of characteristic with respect to frequency but for any specified fre- (ill This is readily seen since the transforming section is in effect equivalent to a uniform section of impedance 1%,, for example, followed by an ideal transformer or voltage ratio qb.

The section therefore operates as if it had different iterative impedances at its opposite terminals, the impedances being in the ratio 5 By definition, however, the iterative impedance of a network is the impedance it exhibits when terminated at its remote terminals by an infinite line of repeated sections, or, in other words, when terminated by its own iterative impedance. But the transforming section is not intended to operate under this condition, consequently its actual iterative impedances have not great significanoe.

Under the ideal operating conditions described above the transforming section couples together two infinite filters without there resulting any reflection losses at the junctions.

There are therefore two impedances which may be used to terminate the unsymmetrical section, one at the one end and one at the other end, so as to produce a system free from reflection loss. These impedanceshave been termed the image impedances of the section.

It has been shown in one of the references already mentioned, Transmission characteris tics of wave filters-O. J. Zobel, Bell System Technical Journal, Volume III, No. 4 October, 1924, that the image impedance or one end of a four terminal network is the geometric mean of the open circuit and short circuit impedances measured at that end. Theimage impedances are these characteristic properties of the network itself without reference to any system in which it may be connected. In the special case of a symmetrical network the image and the iterative impedances are identical.

For efiicient operation the transforming section should be terminated in its own image impedances or in physical impedance structures that furnish a satisfactory approximation thereto. Successive transforming sections may be connected in tandem and each may have the same transformation ratio or different ratios may be employed but each succeeding section must start off from the impedance reached by the preceding one in order that reflection losses may be avoided.

In general sections having equal image impedances may be joined together to form any desired sequence, just as in tlie case of symmetrical filters sections having equal iterative impedances may be joined together.

In considering the flow of energy throu h .these wave transforming filters it should observed that the electromagnetic force and the current of transmitted waves will be trans! formed in inverse ratios. When the electrifmagnetic force is increased by the ratio being greater than unity the current will be proportionately diminished and vice versa. The resultant electromagnetic force and current at the output end of such a filter may be found by first of all determining, by well known methods, the values that would result if the whole system were, designed uniformly for the image impedance at the input end and then applying a single transformation ratio equal to the product of all thetransformation ratios used in the system to the values so computed.

. From thepreceding explanation the transforming properties and the computation of the additional sections will be readily understood and the description of these will be limited to their most important characteristic features.

Formulae relating to the design of the symmetrical,- or non-transforming, filters from which the individual transforming sections may be derived are given by O. J. Zobel, Theory and design of uniform and composite electric wave filters, Bell System Technical Journal, Vol. II, No. 1, January, 1923, reference be ng made particularly to Appendix II, Sections IV to XI inclusive.

In Flgures 4 and 5 as in Fig. 3 the symbols deslgnate the coefficients of the unsymmetrical transforming network. The coefficients of the symmetrical structures corresponding to these will be denoted by the same symbols accompamed by a prime mark. The symmetrical prototypes o Figs t and 5 have the same structural arrangements of elements as the transforming sections. In each case it will be assumed that the symmetrical prototy e is designed to match the lower impedance 5,.

In the network of Fig. 4 the series inductance is the basis of the transformation, and the shunt inductanccs of the II type transformer equivalent are combined with the natural shunt inductances of the section to give the final inductances L and L Followin the method outlined in connectlon with Fig.3 the coefiicients of Fig. 4 may be written down in terms of the coeflicients of the symmetrical prototype. The values folfor which condition the inductance may be dropped from the circuit.

In the section shown in Fig. 5 the series I For one value of the transformation ratio the inductance L becomes infinite, and becomes negative when this value is exceeded. The capacity 0 becomes zero for another value of the ratio and negative for greater values. The limiting value of the transformation ratio is the lower of the two initial 7 values.

The sections shown in Figs. 6 and 7 are based on the symmetrical prototype shown in Fig. 8. That of Figure 6 is derived from the prototype b making the series inductance L the basis 0 the transformation.- I

It follows from Equation ('1) that there can only be a step down transformation in the direction from Z to Z otherwise the inductance L which corresponds to Z, of Fig. 2, would be ne ative and .the network would be impractica 1c. The limiting value of the transformation ratio is that which makes the inductance .1 infinite, this being the inductance in which the negative element of the transformer equivalent isvincluded.

The coefiicients of the network of Fig. 6 are given interms ofthe coeflicients of the prototype network of'Fig.8 and the transformation ratio, by the following equations The remaining coeflicients U L and 0. difierfrom the corresponding ,protot pe coefiicients in the ratio the capacities and the inductance being changedf rih, inverse 1 ratios.

procedure would be muc In Fig. 7 is shown a second transforming network based on the prototype network of Fig. 8 but in this instance the series capacity 0 is used to give the transformer equivalent. This type of network must have a voltage step-up between Z and Z in order that the capacity 0,, may be positive. The limiting value of the ratio is that which reduces to zero the value of capacity 0 which analogously to L of Fig. 6, is the element that includes the negative element of the transformer equivalent. The relationships between the elements of the transforming network and its symmetrical prototype may be derived by the methods alread Y described.

The wave filter sections of igs. 3 to 8 in- I elusive are all of the mid-shunt type but the invention is not confined to this type alone as is illustrated by the exam le of a mid series transforming section of i 9 and its symmetrical prototype shown in i 10.

The shunt branch impedance ofh igs. 9 and 10 differs from those of the other sections in that it includes one parallel branch consisting of a series resonant circuit. It might appear that since the series branches of I ig. 10 also consist of series resonant circuits the transformer equivalent might be based upon one complete series branch rather than on a single element. But while it is true that a pair of simple anti-resonant circuits connected in parallel may be re laced by a single anti-resonant circuit, and that two series resonant circuits connected in series are equivalent to a single resonant combination, it is not possible to replace a combination of two series resonant circuits in parallel by a single resonant circuit.

In Fig. 9 the transformation is based on the series inductance L of the prototype network, the transformer equivalent comprising L L and a negative component combined in The foregoing description of the various examples of wave transforming filter sections discloses a general method of. effecting wave transformation which is capable of application in many types of circuits besides those illustrated. The design procedure disclosed calls for the design in the first place of a non-transforming system having the desired energy propagation characteristics; it would be possible to derive formulaa in each case for the direct com utation but such a more complicated.

urther, since the design of uniform, nontransforming systems is already a well-known art, any direct method of design would be less easily understood and applied than one basled on a simple addition to the known prin- 01p es.

As has alreadybeen pointed out the transormer equivalent II network does not have a separate embodiment but it nevertheless the wave transforming section of Fig. 3 is shown in Fig. 11. The circuit illustrated represents a portion of a radio receiving system designed to operate in accordance with the so-called super=heterodyne principle. Space discharge device 1 is a demodulator, or detector upon which are simultaneously impressed a modulated wave of carrier frequency f representing the received radio wave, and an auxiliary wave of frequency fb derived from a local source. The derived demodulation products are the carrier Wave of intermediate frequency f -f and the accompanying side frequencies corresponding to the modulations of the received radio wave. The wave filter included between the output terminals of 1 and the input terminals of a second space discharge device 2 is designed to select the desired waves and at the same time to step them up in voltage. By virtue'of its band-pass properties the filter transmits all components of the intermediate frequency -waves with equal efficiency and suppresses all other waves.

Space discharge tube 2 is an amplifier for" the intermediate frequency waves and may be followed by additional stages coupled by similar selective circuits before the final detection of the signals is effected.

The filter is designed-to transmit waves between the limiting frequencies 45000 c. p. s.

and 55000- c. p. s. and to be terminated at its input end in a resistance of 20,000 ohms, the

space path resistance of demodulator 1. The requirements as to selectivity were such as to make it. necessary to use two complete filter sections.

In order that the final filter elements may have such values as would render their manufacture simple and economical bot-h sections have been designed as wave transfornnn sec- 'tions, the resultbeing uivalent to the mserthe input capacity of amplifier 2 was .re--

quired to function as the final capacity 6' a fixed valve of 20 micro-microfarad being found to be the propervalue. Satisfactory 'values of the transformation ratios were found by successive approximations, the

' values finally chosen being The first transformation actually stepsdown (41) and (6) gave thefollowing values for the coefficient.

Capacity 0,, functions verily as a low impedance shunt to the space current battery, and it should have a large capacity, for example 2 microfarads, so that its impedance is negligibly small at the frequencies of the waves transmitted through the filter.

What is claimed is:

1. An impedance transforming wave filter having a broad band pass characteristic, characterized in this that the filter includes as animpedance transforming means of constant transformation ratio a 7r network of impedances, at least one of the shunt impedances of the 1r network beingcombined with an adjacentshunt branch of the filter.

2. An impedance transforming..wave filter includin as an impedance transforming means o constant transformation ratio a 1r network whose branches comprise similar impedances the coefficients ofwhich are related by functions of the im edance transformation ratio,-at least one 0 the shunt impedances' that the portions of the wave filteron opposite sides of the transforming means are proportioned to unequal characteristic impedanc'es whose values are in the same ratio. v

as the impedance transformation ratio of the transforming means. I

4. An impedance transforming wave filter havin a broad band pass characteristic, and including as an impedance transformin means a r network comprising shunt impe' ances Z and Z}, and a seriessimpedance Z the values of which impedances are related by the equations Z Z :1a Z..= p in which I is the square root of the impedance transformation ratio, and at least one.

having a broad band pass "characteristic, and

'of said shunt impedances 'being co'mbined with an' adjacent shunt 'impedanceof the jfilterp 5. An impedance transforming wave filter in accordance with claim 4 characterized in this thatthe series impedance of the transforming network comprises a single reactive element, the shunt impedances comprising similar elements, one of which has a negative coefficient said ne ative element being combined with a simi ar positive element in an adjacent shunt impedance of the filter.

6; An impedance transforming wave filter in accordance with claim 4, characterized in this that the series impedance of the transforming network is a capacity, the shunt im- 10 pedances being respectively positive and negain accordance with claim 4, characterized in this that the portions of the wave filter on opposite sides of the transforming network are proportioned to characteristic impedances which are unequal and in the constant ratio Q. -8. An unsymmetrical wave filter section comprising two une ual shunt impedances proportionally related at all frequencies in a constant ratio which is dilfercnt from unity,-in combination with a II type coupling network com rising series and shunt impedances of simi ar type and of such values that their algebraic sum is zero, the shunt impedances of said coupling network being of opposite sign, and their magnitudes being related in the ratio whereby waves may be transmitted without loss due to reflection between terminal impedances whose values are in the constant ratio In witness whereof, I hereunto subscribe my name this 11 day of May, A. D., 1925.

EDWARD L. NORTON. 

